Question
Colette ran 2 laps on Monday, 4 laps on Tuesday, 8 laps on Wednesday, and 16 laps on Thursday. What kind of sequence is this?
Answers
GPT-4o mini
The number of laps Colette ran each day forms a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant factor.
In this case:
- Monday: 2 laps
- Tuesday: 4 laps (2 * 2)
- Wednesday: 8 laps (4 * 2)
- Thursday: 16 laps (8 * 2)
The common ratio is 2, since each day's laps are double the number of laps from the previous day. Therefore, the sequence can be expressed as:
\( a_n = 2^n \)
where \( n \) starts from 1 (representing Monday) up to 4 (representing Thursday). Thus, the sequence is geometric with a common ratio of 2.
In this case:
- Monday: 2 laps
- Tuesday: 4 laps (2 * 2)
- Wednesday: 8 laps (4 * 2)
- Thursday: 16 laps (8 * 2)
The common ratio is 2, since each day's laps are double the number of laps from the previous day. Therefore, the sequence can be expressed as:
\( a_n = 2^n \)
where \( n \) starts from 1 (representing Monday) up to 4 (representing Thursday). Thus, the sequence is geometric with a common ratio of 2.